Remark 3.3 
A horizontal distribution on a symplectic fibration such that the corresponding parallel transport preserves the fiberwise symplectic structure is also called a symplectic connection (see for example [1]}). The symplectic affine connections considered here are symplectic connections in this more general sense, although the converse is clearly false. For this reason (and also to honor their role in Fedosov's deformation quantization) what are here called symplectic connections are sometimes called Fedosov connections; here the notions are distinguished terminologically as linear and nonlinear symplectic connections.
